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Stochastic grey-box models in a Bayesian and fuzzy perspective for occupancy estimation in buildings under uncertainty.

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Title: Stochastic grey-box models in a Bayesian and fuzzy perspective for occupancy estimation in buildings under uncertainty.
Authors: Korkidis, Panagiotis1 (AUTHOR) p.korkidis@uniwa.gr, Dounis, Anastasios1 (AUTHOR) aidounis@uniwa.gr, Santamouris, Mattheos2 (AUTHOR) m.santamouris@unsw.edu.au
Source: Energy & Buildings. May2026, Vol. 358, pN.PAG-N.PAG. 1p.
Subjects: Stochastic differential equations, Bayesian analysis, Hidden Markov models, Intelligent buildings, Fuzzy algorithms, Estimation theory, Carbon dioxide detectors, Measurement uncertainty (Statistics)
Abstract: • Stochastic differential equations and Bayesian techniques for uncertainty assessment. • Stochastic and hidden Markov models within an occupancy estimation framework. • Fuzzy approach to stochastic differential equations for uncertainty quantification. This study explores the problem of occupancy estimation in buildings, focusing on the notion of uncertainty. Two types of uncertainty are considered: parametric and non-parametric. The former stems from imprecise knowledge of model parameters, while the latter arises from stochastic factors. The objective is to estimate the number of occupants based on carbon dioxide observations, while also examining the impact of uncertainty on this estimation. The carbon dioxide concentration is modeled by a diffusion process, which emerges as the solution to the stochastic mass-balance differential equation with unknown parameters. In light of this, we propose two different approaches to the problem: a Bayesian framework, which enables the generation of posterior distributions for the unknown parameters, and a fuzzy modeling approach that treats the model parameters as fuzzy numbers and addresses the problem on a fuzzy stochastic differential equations basis. In the Bayesian approach, a Markov Chain Monte Carlo method, specifically slice sampling, is used to derive samples from the posterior distributions of the parameters. The occupancy level is estimated within a hidden Markov model framework, where the potential number of occupants is considered as a latent state that generates the observed carbon dioxide levels. To enhance the accuracy and efficiency of occupancy estimation, we integrate the Viterbi algorithm. Consequently, we investigate the influence of uncertainty on the estimation process, providing insights into its implications for occupancy assessment in smart buildings. The proposed method achieves a minimum accuracy of 98% in estimating occupancy sequences across all synthetic and real-world data considered. [ABSTRACT FROM AUTHOR]
Copyright of Energy & Buildings is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
An: 192226613
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  Data: Stochastic grey-box models in a Bayesian and fuzzy perspective for occupancy estimation in buildings under uncertainty.
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  Data: • Stochastic differential equations and Bayesian techniques for uncertainty assessment. • Stochastic and hidden Markov models within an occupancy estimation framework. • Fuzzy approach to stochastic differential equations for uncertainty quantification. This study explores the problem of occupancy estimation in buildings, focusing on the notion of uncertainty. Two types of uncertainty are considered: parametric and non-parametric. The former stems from imprecise knowledge of model parameters, while the latter arises from stochastic factors. The objective is to estimate the number of occupants based on carbon dioxide observations, while also examining the impact of uncertainty on this estimation. The carbon dioxide concentration is modeled by a diffusion process, which emerges as the solution to the stochastic mass-balance differential equation with unknown parameters. In light of this, we propose two different approaches to the problem: a Bayesian framework, which enables the generation of posterior distributions for the unknown parameters, and a fuzzy modeling approach that treats the model parameters as fuzzy numbers and addresses the problem on a fuzzy stochastic differential equations basis. In the Bayesian approach, a Markov Chain Monte Carlo method, specifically slice sampling, is used to derive samples from the posterior distributions of the parameters. The occupancy level is estimated within a hidden Markov model framework, where the potential number of occupants is considered as a latent state that generates the observed carbon dioxide levels. To enhance the accuracy and efficiency of occupancy estimation, we integrate the Viterbi algorithm. Consequently, we investigate the influence of uncertainty on the estimation process, providing insights into its implications for occupancy assessment in smart buildings. The proposed method achieves a minimum accuracy of 98% in estimating occupancy sequences across all synthetic and real-world data considered. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Data: <i>Copyright of Energy & Buildings is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Type: doi
        Value: 10.1016/j.enbuild.2026.117232
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      – Code: eng
        Text: English
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      – SubjectFull: Stochastic differential equations
        Type: general
      – SubjectFull: Bayesian analysis
        Type: general
      – SubjectFull: Hidden Markov models
        Type: general
      – SubjectFull: Intelligent buildings
        Type: general
      – SubjectFull: Fuzzy algorithms
        Type: general
      – SubjectFull: Estimation theory
        Type: general
      – SubjectFull: Carbon dioxide detectors
        Type: general
      – SubjectFull: Measurement uncertainty (Statistics)
        Type: general
    Titles:
      – TitleFull: Stochastic grey-box models in a Bayesian and fuzzy perspective for occupancy estimation in buildings under uncertainty.
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            NameFull: Korkidis, Panagiotis
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            NameFull: Dounis, Anastasios
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            NameFull: Santamouris, Mattheos
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            – D: 01
              M: 05
              Text: May2026
              Type: published
              Y: 2026
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              Value: 358
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